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8.1 Inverse Trigonometric Functions

In this section, we will study the following topics:

Definitions of the inverse trig functions

Evaluating inverse sine, cosine, and tangent functions by hand and using the calculator.

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Summary of the Inverse Trig Functions

Function Domain Range

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sin sin 1 12 2

cos cos 1 1 0

tan tan2 2

y x iff x y x y

y x iff x y x y

y x iff x y x y

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Evaluate the following inverse trig functions without using the

calculator. Give the exact answer in radians, in terms of .

1 111. sin 2. sin 1

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Examples

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1 1 23. cos 0 4. cos

2

Evaluate the following inverse trig functions without using the

calculator. Give the exact answer in radians, in terms of .

Examples

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1 15. tan 1 6. tan 3

Examples

Evaluate the following inverse trig functions without using the

calculator. Give the exact answer in radians, in terms of .

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Evaluate the following inverse trig functions using the

calculator. Give your answer in degrees, to the nearest tenth.

1 137. tan 8. sin 2.64

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Examples

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1 1 59. cos 0.15 10. tan

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Examples

Evaluate the following inverse trig functions using the

calculator. Give your answer in degrees, to the nearest tenth.

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Example

End of Section 8.1

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